Dissertations / Theses on the topic 'Double layer potential'

Layer potential operators associated to elliptic partial differential equations have been an object of investigation for more than a century, due to their contribution in the solution of boundary value problems through integral equations. In this Licentiate thesis we prove the boundedness of the double layer potential operator on the Hilbert space of square integrable functions on the boundary, associated to second order uniformly elliptic equations in divergence form in the upper half-space, with real, possibly non-symmetric, bounded measurable coefficients, that do not depend on the variable transversal to the boundary. This uses functional calculus of bisectorial operators and is done through a series of four steps. The first step consists of reformulating the second order partial differential equation as an equivalent first order vector-valued ordinary differential equation in the upper halfspace. This ordinary differential equation has a particularly simple form and it is here that the bisectorial operator corresponding to the original divergence form equation appears as an infinitesimal generator. Solving this ordinary differential through functional calculus comprises the second step. This is done with the help of the holomorphic semigroup associated to the restriction of the bisectorial operator to an appropriate spectral subspace; the restriction of the operator is a sectorial operator and the holomorphic semigroup is well-defined on the spectral subspace. The third step is the construction of the fundamental solution to the original divergence form equation. The behaviour of this fundamental solution is analogous to the behaviour of the fundamental solution to the classical Laplace equation and its conormal gradient of the adjoint fundamental solution is used as the kernel of the double layer potential operator. This third step is of a different nature than the others, insofar as it does not involve tools from functional calculus. In the last step Green’s formula for solutions of the divergence form partial differential equation is used to give a concrete integral representation of the solutions to the divergence form equation. Identifying this Green’s formula with the abstract formula derived by functional calculus yields the sought-after boundedness of the double layer potential operator, for coefficients of the particular form mentioned above.

Abstract The dissertation considers the time fractional diffusion equation (TFDE) with the Dirichlet boundary condition in the sub-diffusion case, i.e. the order of the time derivative is α ∈ (0,1). In the thesis we have studied the solvability of TFDE by the method of layer potentials. We have shown that both the single layer potential and the double layer potential approaches lead to integral equations which are uniquely solvable. The dissertation consists of four articles and a summary section. The first article presents the solution for the time fractional diffusion equation in terms of the single layer potential. In the second and third article we have studied the boundary behaviour of the layer potentials for TFDE. The fourth paper considers the spline collocation method to solve the boundary integral equation related to TFDE. In the summary part we have proved that TFDE has a unique solution and the solution is given by the double layer potential when the lateral boundary of a bounded domain admits C1 regularity. Also, we have proved that the solution depends continuously on the datum in the sense that a nontangential maximal function of the solution is norm bounded from above by the datum in L2(ΣT). If the datum belongs to the space H1,α/2(ΣT), we have proved that the nontangential function of the gradient of the solution is norm bounded from above by the datum in H1,α/2(ΣT).

Water scarcity is a global concern that impacts many developing countries, forcing people to depend on unclean water sources for domestic, agricultural, and industrial needs. Wastewater is an alternative water source that contains nutrients needed for crop growth. Wastewater reuse for agriculture can cause public health problems because of human exposure to pathogens. Pathogen monitoring is essential to evaluate the compliance of wastewater with established World Health Organization (WHO) and U.S. Environmental Protection Agency (EPA) wastewater reuse guidelines. Indicator organisms are commonly used to detect pathogens in water and wastewater because they are quick and easy to measure, non-pathogenic, and have simple and inexpensive methods of detection. The objective of this research was to develop a modified double agar layer assay method that can be conducted in the field to quantify bacteriophage to assess the quality of wastewater for agricultural reuse. Results from the modified double agar layer assay were used to investigate the potential of somatic coliphage as an indicator organism for assessing the potential presence of enteric viruses in developing world treated wastewater, and to use the criteria of a good indicator organism to compare the potential of two commonly used indicator organisms, somatic coliphage and fecal coliforms, as an indicator of enteric viruses in wastewater. A modified EPA double agar layer method was developed and deployed in a developing world rural community to effectively quantify the concentration of somatic coliphage in a community managed wastewater treatment system composed of a Upflow Anaerobic Sludge Blanket (UASB) reactor followed by two maturation lagoons. The modified method served as a good indicator of enteric viruses in the water. Somatic coliphages were easily detected and quantified in the field setting using a modified double agar layer method. Somatic coliphage was found to be a potential indicator for enteric viruses rather than fecal coliforms because of their similarity in characteristics and resistances to wastewater treatment. The concentration of somatic coliphage was only reduced by 1.05 log units across the two series maturation lagoon system. Previous literature suggested removal would range from 2.1 to 4.6 log units. Influent wastewater (previously treated by an UASB reactor) had a concentration of 4.38 E+06 PFU/ 100 mL (standard deviation = ±3.7E+06, n = 9) and the treated effluent contained 3.90 E+05 PFU/100 mL (standard deviation = ± 4.5E+05, n = 8) of somatic coliphages. Results suggest that somatic coliphage is a good potential indicator for enteric viruses in wastewater but further research needs to be done.

We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.

The Double-TOP trap is a new type of magnetic trap for neutral atoms, and is suitable for Bose-Einstein condensates (BECs) and evaporatively cooled atoms. It combines features from two other magnetic traps, the Time-averaged Orbiting Potential (TOP) and Ioffe-Pritchard traps, so that a potential barrier can be raised in an otherwise parabolic potential. The cigar-like cloud of atoms (in the single-well configuration) is divided halfway along its length when the barrier is lifted. A theoretical model of the trap is presented. The double-well is characterised by the barrier height and well separation, which are weakly coupled. The accessible parameter space is found by considering experimental limits such as noise, yielding well separations from 230 [mu]m up to several millimetres, and barrier heights from 65 pK to 28 [mu]K (where the energies are scaled by Boltzmann�s constant). Potential experiments for Bose-Einstein condensates in this trap are considered. A Double-TOP trap has been constructed using the 3-coil style of Ioffe-Pritchard trap. Details of the design, construction and current control for these coils are given. Experiments on splitting thermal clouds were carried out, which revealed a tilt in the potential. Two independent BECs were simultaneously created by applying evaporative cooling to a divided thermal cloud. The Double-TOP trap is used to form a linear collider, allowing direct imaging of the interference between the s and d partial waves. By jumping from a double to single-well trap configuration, two ultra-cold clouds are launched towards a collision at the trap bottom. The available collision energies are centred on a d-wave shape resonance so that interference between the s and d partial waves is pronounced. Absorption imaging allows complete scattering information to be collected, and the images show a striking change in the angular distribution of atoms post-collision. The results are compared to a theoretical model, verifying that the technique is a useful new way to study cold collisions.

This master´s thesis deals different types of the aprotic electrolytes for supercapacitors and investigates by impedance spectroscopy to conductivity and method cyclic voltametry to measure dimension potential windows. Used aprotic solvents: propylencarbonate, dimethylsulfoxide, N, N dimethylformamide, ethylencarbonate, dimethylcarbonate, diethylcarbonate and acetonitrile. In the aprotic solvents were appended salts: LiClO4, NaClO4, KClO4, LiBF4, LiPF6, TEABF4 and TMABF4. From these compounds were prepared solutions with the different molar concentrations.

This master’s thesis deals with supercapacitors and polymer gel electrolytes. The practical part deals with the preparation of samples of polymer gel electrolyte with addition of alkali salts by measuring their electrical conductivity and evaluation potential windows.

La limitation des rejets en CO₂ associés aux normes européennes antipollution de plus en plus sévères ont conduit les constructeurs automobiles à innover dans de nouveaux concepts de combustion, dans l’objectif d’augmenter le rendement des moteurs essence conventionnels. La combustion de type Partiellement Prémélangée, communément appelée Gasoline Partially Premixed Combustion (soit GPPC) semble être l’un des possibilités pour répondre à ces problématiques, en particulier s’il était possible d’atteindre un rendement proche des rendements Diesel avec des émissions polluantes plutôt de type moteur à allumage commandé et qui pourraient donc être traitées par systèmes de post-traitement classiques. Cette étude vise, par une approche expérimentale, à comprendre les processus physiques qui permettent d’optimiser ce nouveau mode de combustion, en particulier en termes de préparation du mélange et de déroulement de la combustion proprement dite. La première partie de ce travail a consisté en la détermination de l’impact des différentes conditions thermodynamiques, de la stratégie d’injections et du taux de dilution sur le déroulement de la combustion à partir de données obtenues sur un moteur opaque. Trois modes de dégagements de chaleur très distincts ont été sélectionnés, l’un représentant la configuration optimale en termes de rendement et d’émissions polluantes à partir d’expériences réalisées sur moteur monocylindre à fort taux de compression et avec une chambre typée Diesel. Des techniques de diagnostics optiques ont été mises en place sur un moteur identique mais à accès optiques dans l’objectif d’isoler tout particulièrement l’impact du phasage de la seconde injection sur le déroulement de la combustion. L’étude de la propagation liquide du spray lors de l’injection, de l’interaction entre l’air et le carburant lors du processus de formation du mélange et de la phase d’oxydation du carburant a ainsi pu être réalisée et a permis de valider les hypothèses émises lors des essais sur moteur opaque pour expliquer les processus de combustion et donner des pistes de contrôle de ce type de combustion
Carbon dioxide (CO₂) and other pollutant emission limitations are more and more rigorous. These limits conduct cars manufacturers to study new combustion concept, in order to increase conventional gasoline engine efficiencies. Gasoline Partially premixed combustion concept (GPPC) seems to have the potential to reach these objectives, in other terms an efficiencies comparable to diesel engine by with emissions of gasoline engine, which mean a low cost after-treatment system. This study investigates, by an experimental approach, the physical process responsible on controlling this combustion concept and by the way improves it. This will be done by studying the mixture preparation and the combustion behaviour. The first part of this work concerns on determining the impact of in-cylinder thermodynamic conditions, injection strategy and the dilution rate on combustion behaviour using a single cylinder all metal engine. Three distinctive heat release rates were selected; where one represent the optimized injection phasing in term of efficiencies and pollutant emissions. The second part was dedicated to studying the process involved in GPPC combustion mode by optical diagnostic techniques on single cylinder optical access diesel engine. The impact of second injection phasing, fuel and air interaction and also the fuel combustion process allowed the validation of hypothesis emitted in the first part to explain the combustion behaviour and give ways to control this combustion mode

The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.

Le saumon Atlantique fait partie du patrimoine écologique et économique du bassin de l’Adour. Dans le cadre de la gestion actuelle du saumon dans ce bassin, l’origine natale des géniteurs, le taux de retour des individus d’origine piscicole, le taux de homing sur chaque sous-bassin ou encore le soutient par des géniteurs extérieurs au bassin de l’Adour sont des thématiques qui restent sans réponses. Ce projet propose donc de tester le potentiel de la géochimie des otolithes sur le saumon Atlantique du bassin de l’Adour. Nos travaux démontrent que la variation géographique de la composition chimique de l’eau dans 12 rivières colonisées par le saumon, associée à un enregistrement dans l’otolithe proportionnel à la signature géochimique du milieu de vie, permettent de discriminer l’origine géographique des individus. La combinaison des signatures élémentaires (Sr:Ca et Ba:Ca) et surtout l’isotopie du Sr (temporellement plus stable et sans fractionnement biologique) dans les otolithes améliore la précision du classement à l’échelle de la rivière de développement. En se basant sur la transmission de signatures géochimiques (élémentaires et isotopiques) transgénérationelles entre la femelle reproductrice et les otolithes des embryons produits par cette dernière, nous avons discriminé avec succès les individus nés en rivière de ceux nés en pisciculture. Le classement des géniteurs (180 individus) selon leur rivière natale a confirmé que le sous bassin du gave d’Oloron, et plus particulièrement le gave d’Ossau, reste le lieu qui produit le plus de saumon de retour. De façon non négligeable, le gave de Pau contribue lui aussi au renouvellement de la population (10 d’origine piscicole et 6 d’origine naturelle). 18 saumons sur 180 sont issus de l’alevinage (soit 10%); la majorité s’étant développée dans le sous-bassin du gave de Pau. Par ailleurs, nous avons mis à jour l’existence de périodes au cours de la vie des juvéniles (changements de milieu: sac vitellin—milieu extérieur et pisciculture—rivière) durant lesquelles l’enregistrement du Ba dans l’otolithe n’est pas en relation avec la chimie de l’eau. L’originalité de notre approche est d’avoir étudié l’influence des facteurs endogènes et environnementaux chez des poissons ayant vécu dans le milieu naturel ou ayant séjourné en milieu naturel contrôlé. Nos travaux mettent l’accent sur la complexité de l’intégration du rapport Ba:Ca dans l’otolithe et démontrent l’utilité des éléments traces et des isotopes du Sr comme « tag naturel » pour distinguer l’origine natale du saumon Atlantique
The Adour basin holds one of the largest populations of Atlantic salmon in southern Europe exploited by commercial and sport fisheries. Determining the relative contributions of individual rivers and hatcheries to the Adour basin populations becomes crucial to understand key sources that contribute the most to its persistence. We successfully used Sr:Ca, Ba:Ca and 87Sr:86Sr ratios as natural tags for determining the natal origins of adults from 12 tributaries. Success in discriminating between fish from different sites was greatest using Sr isotopes since the latter remained relatively constant across years at a given location. Geochemical signatures from core regions of the otolith were also used to identify fish from hatchery or naturally spawned sources. The predominance of adults spawned in the Ossau River among returning adults corresponded with long-term juvenile production trends in the Ossau River. Despite the limited upstream accessibility of the Pau River, our study demonstrated that Atlantic salmon recruits can successfully leave this river to join the adult population in the Adour basin. We observed relatively clear separation between hatchery and wild juveniles using both Sr:Cacore (wild > 2.5 and hatchery < 0.80) and 87Sr:86Srcore (wild < 0.710 and hatchery > 0.710). The return of hatchery reared fish as adult spawners represented 10% of the total sampled fish we analyzed. Almost all adults, previously identified as belonging to the Ouzom River, were hatchery produced. Adults originated from the Pau River were either wild or hatchery reared fish. We also conducted field controlled experiments that characterized the elemental uptake process in juvenile Atlantic salmon otoliths during freshwater residency. Physiological effects influenced Ba deposition. Ba:Ca otolith profiles from hatchery-reared and field collected fish were characterised by a peak at yolk absorption mark. Hatchery-reared fish stocked in a river also displayed a peak of Ba:Ca following transfer which was not related to the water chemistry. Our experiment revealed a 20-day lag time between initial Ba:Cawater changes and Ba:Caotolith saturation. Results suggested that such effects should be considered during any attempts to determine rivers of origin of Atlantic salmon based on otolith elemental composition or reconstruct the movement of individual fish among and within streams

Particle suspensions occur in many situations in nature and industry. In this master’s thesis, the motion of a single rigid spheroidal particle immersed in Stokes flow is studied numerically using a boundary integral method and a new specialized quadrature method known as quadrature by expansion (QBX). This method allows the spheroid to be massless or inertial, and placed in any kind of underlying Stokesian flow.   A parameter study of the QBX method is presented, together with validation cases for spheroids in linear shear flow and quadratic flow. The QBX method is able to compute the force and torque on the spheroid as well as the resulting rigid body motion with small errors in a short time, typically less than one second per time step on a regular desktop computer. Novel results are presented for the motion of an inertial spheroid in quadratic flow, where in contrast to linear shear flow the shear rate is not constant. It is found that particle inertia induces a translational drift towards regions in the fluid with higher shear rate.
Partikelsuspensioner förekommer i många sammanhang i naturen och industrin. I denna masteruppsats studeras rörelsen hos en enstaka stel sfäroidisk partikel i Stokesflöde numeriskt med hjälp av en randintegralmetod och en ny specialiserad kvadraturmetod som kallas quadrature by expansion (QBX). Metoden fungerar för masslösa eller tröga sfäroider, som kan placeras i ett godtyckligt underliggande Stokesflöde.   En parameterstudie av QBX-metoden presenteras, tillsammans med valideringsfall för sfäroider i linjärt skjuvflöde och kvadratiskt flöde. QBX-metoden kan beräkna kraften och momentet på sfäroiden samt den resulterande stelkroppsrörelsen med små fel på kort tid, typiskt mindre än en sekund per tidssteg på en vanlig persondator. Nya resultat presenteras för rörelsen hos en trög sfäroid i kvadratiskt flöde, där skjuvningen till skillnad från linjärt skjuvflöde inte är konstant. Det visar sig att partikeltröghet medför en drift i sidled mot områden i fluiden med högre skjuvning.

Electroosmotic flow is a convenient mechanism for transporting polar fluid in a microfluidic device. The flow is generated through the application of an external electric field that acts on the free charges that exists in a thin Debye layer at the channel walls. The charge on the wall is due to the chemistry of the solid-fluid interface, and it can vary along the channel, e.g. due to modification of the wall. This investigation focuses on the simulation of the electroosmotic flow (EOF) profile in a cylindrical microchannel with step change in zeta potential. The modified Navier-Stoke equation governing the velocity field and a non-linear two-dimensional Poisson-Boltzmann equation governing the electrical double-layer (EDL) field distribution are solved numerically using finite control-volume method. Continuities of flow rate and electric current are enforced resulting in a non-uniform electrical field and pressure gradient distribution along the channel. The resulting parabolic velocity distribution at the junction of the step change in zeta potential, which is more typical of a pressure-driven velocity flow profile, is obtained.
Singapore-MIT Alliance (SMA)

碩士
國立臺灣科技大學
機械工程系
103
With the advance of the nano technology, nowadays there are more and more materials and devices which are relevant to nano dimension. This study deals with electric double layer (EDL) potential at solid/electrolyte interface within nano dimension. The measurement of EDL potential is typically achieved by using the atomic force microscope (AFM), the mathematical model of surface force, and the Matlab software. The surface force was regard as sum of Van der waals force and electrostastic force by setting up low probe velocity. In addition the surface of sample was modified by chemical mechanical polishing (CMP) process. The simulation results of Comsol software with Poisson Boltzmann、Modified Poisson Boltzmann equations show that this methodology is valid. These surface force experiments found that the thickness of stern layer could be 0.68 to 0.78 nanometer. The zeta potential are -33, -10, millivolt respectively in NaCl and MgCl2 electrolyte with Au surface, and the zeta potential are 23, 8 milivolt respectively in NaCl and MgCl2 electrolyte with glass wafer. In the end, according to lately literatures, the range of zeta potential is from -32 to -67 milivolt with Au surface, and the zeta potential in this study is -33 milivolt. It shows that under these conditions, like good surface roughness, well probe setting, the electric double layer potential at solid/electrolyte interface within nano dimension can measured by AFM device and mathematical software.

碩士
國立臺灣科技大學
纖維及高分子工程技術研究所
85
Part Ⅰ Ionizable groups in polyelectrolyte gel interact electrostatically with ions in surrounding electrical potential. This work studies the swelling kinetics via water uptake by dry samples and zeta potentials by streaming potential measurement of Poly (vinyl alcohol-g-sodium styrenesulfonate) (PVA-g-SSS) and Poly (acrylonitrile- acrylamide-acrylic acid) (P(AN-AAm-AA)) gels in aqueous KCl solutions. The water absorption increase and then decreases with the concentration of KCl, and the diffusion coefficient of water into dry gels is maximal at the minimum water uptake. The maximum ion shielding on the gel surface occurs to the situation with lowest water uptake at intermediate electrolyte concentrations, and then excess K+ ions enters the swollen network, subsquently being hydrated at the higher electrolyte concentrations. Moreover, the water swelling deviates more significantly from the Fickian mode with the higher electrolyte concentrations, due to hysteresis on the swelling-driven mechanical relaxation caused by the K+. Both gels, have negative zeta potentials, whose absolute value increase with KCl concentration and becomes zero at intermediate KCl concentrations. Such a point-of-zero-charge phenomenon is also a manifestation of ion shielding on the gel at interface. Part Ⅱ The contact angle of air and n-octane on P(AN-AAm-AA) and P(VA-g-SSS) hydrogels in aqueous KCl solutions at 25℃ were measured. The interfacial energy between gels and water decreases with the decreasing water content of gels. The water content of gels decreases and then increases with the concentration of surrounding KCl solutions, and the minimum point implies the maximum shielding on the gel surface, maximum water-gel interaction energy at interface, and minimum interfacial energy. The relations between zeta potential of gel interface and interfacial energy of gels leads to the conclusions that the surface charge density of gels decreases with the ion content of gel bulk, and the capacity of electrical double layer is non-zero. The valence data of mobile ions in diffuse layer indicate that the permeability of gel interface make the electrical behavior of gel-ion interface different from the rigid interface.

The sequence-dependent curvature and flexibility of DNA is critical for many biochemically important processes. However, few experimental methods are available for directly probing these properties at the base-pair level. One promising way to predict these properties as a function of sequence is to model DNA with a set of base-pair parameters that describe the local stacking of the different possible base-pair step combinations. In this dissertation research, we develop and study a computational model for predicting the diffusion coefficients of short, relatively rigid DNA fragments from the sequence and the base-pair parameters. We focus on diffusion coefficients because various experimental methods have been developed to measure them. Moreover, these coefficients can also be computed numerically from the Stokes equations based on the three-dimensional shape of the macromolecule. By comparing the predicted diffusion coefficients with experimental measurements, we can potentially obtain refined estimates of various base-pair parameters for DNA. Our proposed model consists of three sub-models. First, we consider the geometric model of DNA, which is sequence-dependent and controlled by a set of base-pair parameters. We introduce a set of new base-pair parameters, which are convenient for computation and lead to a precise geometric interpretation. Initial estimates for these parameters are adapted from crystallographic data. With these parameters, we can translate a DNA sequence into a curved tube of uniform radius with hemispherical end caps, which approximates the effective hydrated surface of the molecule. Second, we consider the solvent model, which captures the hydrodynamic properties of DNA based on its geometric shape. We show that the Stokes equations are the leading-order, time-averaged equations in the particle body frame assuming that the Reynolds number is small. We propose an efficient boundary element method with a priori error estimates for the solution of the exterior Stokes equations. Lastly, we consider the diffusion model, which relates our computed results from the solvent model to relevant measurements from various experimental methods. We study the diffusive dynamics of rigid particles of arbitrary shape which often involves arbitrary cross- and self-coupling between translational and rotational degrees of freedom. We use scaling and perturbation analysis to characterize the dynamics at time scales relevant to different classic experimental methods and identify the corresponding diffusion coefficients. In the end, we give rigorous proofs for the convergence of our numerical scheme and show numerical evidence to support the validity of our proposed models by making comparisons with experimental data.
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Poor settling of solids increases land requirement for tailings containment and imposes severe constraints on the water balance. Consequent to these considerations, the alternating current electrocoagulation (AC/EC) technique emerged as a candidate for enhancing the settling behaviour of suspensions in the mineral, coal and oil sands industries. Hence, a fundamental study of AC/EC was undertaken with aluminum electrodes. Ground silica (d50 = 20 m), which formed a stable suspension, served as the model tailings solid at 5.0 wt % in water. The AC/EC process consisted of two developmental stages: coagulation, marked by pH decrease in the silica suspension; and floc growth, characterized by pH increase from the minimum (i.e., the end of coagulation). AC/EC enhanced the initial settling rate of silica by over three orders of magnitude, and exhibited remarkable flexibility by virtue of the wide range of process parameters that could be optimized. For example, AC/EC can be operated in either the indirect or direct mode. The settling behaviour of bentonite (estimated d50 < 1 m) was more enhanced by indirect AC/EC, while that of silica benefited more from direct AC/EC. Any condition that increased aluminum dosage (e.g., current, retention time), increased the initial settling rate of silica. Over the feed water pH range of 3.0 to 9.1, AC/EC was effective in enhancing the settling behaviour of silica. AC/EC was also effective over a wide range of temperatures (23 to 85C). High electrical energy demand by AC/EC was observed throughout this study. Its optimization was beyond the scope of this work. Dilution of a sample of Syncrude mature fine tailings (MFT) to 4.6 wt % solids sustained a stable suspension. Settling occurred after AC/EC treatment, a crystal-clear supernatant resulted and bitumen was recovered as froth. Entrained solids were easily spray-washed from the froth with water. The settling behaviour of a Luscar Sterco fine coal tailings sample was not augmented by AC/EC, possibly due to contamination by the companys own electrocoagulation operation. After having been stored dry for more than a year, electrocoagulated silica was an effective coagulant for as-received silica and Syncrude MFT.
Chemical Engineering

The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface, in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.

Ultra-cold dilute gases of neutral atoms are attractive candidates for creating controlled mesoscopic quantum systems. In particular, quantum degenerate gases of bosonic and fermionic atoms can be used to model the correlated many-body behaviour of Bose and Fermi condensed matter systems, and to study matter wave interference and coherence. This thesis describes the experimental realization and manipulation of Bose-Einstein condensates (BECs) of 87Rb and degenerate Fermi gases (DFGs) of 40K using static and dynamic magnetic atom chip traps. Atom chips are versatile modern tools used to manipulate atomic gases. The chips consist of micrometre-scale conductors supported by a planar insulating substrate, and can be used to create confining potentials for neutral atoms tens or hundreds of micrometres from the chip surface. We demonstrate for the first time that a DFG can be produced via sympathetic cooling with a BEC using a simple single-vacuum-chamber apparatus. The large 40K-87Rb collision rate afforded by the strongly confining atom chip potential permits rapid cooling of 40K to quantum degeneracy via sympathetic cooling with 87Rb. By studying 40K-87Rb cross-thermalization as a function of temperature, we observe the Ramsauer-Townsend reduction in the 40K-87Rb elastic scattering cross-section. We achieve DFG temperatures as low as T = 0.1TF , and observe Fermi pressure in the time-of-flight expansion of the gas. This thesis also describes the radio-frequency (RF) manipulation of trapped atoms to create dressed state double-well potentials for BEC and DFG.We demonstrate for the first time that RF-dressed potentials are species-selective, permitting the formation of simultaneous 87Rb double-well and 40K single-well potentials using a 40K-87Rb mixture. We also develop tools to measure fluctuations of the relative atom number and relative phase of a dynamically split 87Rb BEC. In particular, we observe atom number fluctuations at the shot-noise level using time-of-flight absorption imaging. These measurement tools lay the foundation for future investigations of number squeezing and matter wave coherence in BEC and DFG systems.